Counterexample to the Hodge Conjecture

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dc.creatorKim, K. H.
dc.creatorRoush, F. W.
dc.date2006-08-10
dc.date2006-08-22
dc.date.accessioned2026-07-07T07:21:38Z
dc.date.available2026-07-07T07:21:38Z
dc.descriptionWe construct a K3 surface whose transcendental lattice has a self-isomorphism which is not a linear combination of self-isomorphisms over $\mathbb{Q}$ which preserve cup products up to nonzero multiples. Products of it with itself give candidates for counterexamples to the Hodge conjecture which may be of interest. We also study the Kuga-Satake construction in relation to these examples.
dc.descriptionWe no longer claim to have disproved the Hodge conjecture. Section 5 is deleted except for 5.3, and Theorems 6.2,6.3 are deleted
dc.identifierhttps://arxiv.org/abs/math/0608265
dc.identifierhttp://arxiv.org/abs/math/0608265
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/115370
dc.subjectAlgebraic Geometry
dc.subject14C30
dc.titleCounterexample to the Hodge Conjecture
dc.typetext

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